Tuned microwave reflector



Dec. 16, 1952 s. FREEDMAN ETAL 2,622,242

TUNED MICROWAVE REFLECTOR Filed May 9, 1945 '7 Sheets-Sheet 2 IHOP/ZO/VMLLY POl/LQ/ZED FIELDS //V NE/GHBORHOOD 0F BfFZZ-CTOR REHfClZ-DFIELD 0/2507" FIELD I INVENTORS 5amue/ fieedman yGwsfa Fonda fionard/ Qw HM A TTORNEY Dec. 16, 1952 s. FREEDMAN ETAL TUNED MICROWAVE REFLECTORFiled May 9, 1945 PHASE D/SPI. ACEMENT 7 Sheets-Sheet 3 INVENTORS ySamue/ Freedman BY G/uszb Fonda Bonard/ A TTORNZ' Y Dec. 16, 1952 s.FREEDMAN ETAL 2,622,242

TUNED MICROWAVE- REF 'LECTOR Filed May 9, 1945 7 Sheets-Sheet 4 Samue/Freedman y G/usfo 5/709 Bonard/ QW W ATTORNEY Dec. 16, 1952 5, FREEDMANETAL 2,622,242

TUNED MICROWAVE REFLECTOR Filed May 9, 1945 7 Sheets-Sheet 5 uA/sm/mreyWHEN ANGLE F/eoM emseron 70 ANTENNA 0056 N07 EQUAL 5/150770 Ali/61E X F?g. 5

(IA/SYMMETRY WHEN ANTENNA /5 N07 /N X) FMNE INVENTORS Sam'ue/ FreedmanBY 6/2/520 fo/ma Bonami WLW ATTORNEY 16, 2 s. FREEDMAN ETA-L 4 TUNEDMICROWAVE REFLECTOR Filed May 9, 1945 7 Sheets-Sheet 6 E'FLfCTOE STE/P019 VEQT/CALLY POL/LQ/Zfl? FIELD 040.950 PHASE s/y/fr/A/s 5065 Fa J3INVENTORS Samue/ Freedman BYG/usfo Fonda Bonard/ Dc. 16, 1952 s,FREEDMAN ETAL 2,622,242

TUNED MICROWAVE REFLECTOR Filed May 9, 1945 7 Sheets-Sheet 7 Vvr n AVEET/C41Ly POZAE/ZED F /EZOS //V NEIGHBORHOOB 0F REFLECTOk INVENTORSSamue/ Freedman BY 674/5 f0 Fonda Ema/-00 .A TTORNZ'Y Patented Dec. 16,1952 UNITED STATES PATENT OFFICE TUNED IVIICROWAVE REFLECTOR SamuelFreedman, United States Navy, and Giusto Fonda Bonardi, Manhattan Beach,

Calif.

Application May 9, 1945, Serial No. 592,802

11 Claims.

This invention relates to surface microwave refiector's, and physicallyand mathematically solves the problem of boundary condition resultingwhen a reflecting plane is of .finitefi. e. a dimension feasible toprovide) rather than infinite dimension (i. e. a dimension which is notfeasible to l generated by the method and means disclosed inouiicopending application Serial No. 587,544, filed April 10, 1945) withan efliciency comparable to that of an infinite plane.

The reflector of this invention differs from others-previously knownbecause of the phase shifting ends. The ends tend to annul the standingwaves on the reflector and thus avoid undesired radiation proceedingtherefrom.

These phase shifting ends may be used to improve the efliciency of anykind of surface reflector. The term surface reflector includes straight,bent or shaped reflectors (as distinguished from dipole reflectors)associated with transmitting or receiving systems. A flat reflector withphase shifting ends is provided for horizon- 1' wings are tuned or madecorrect for the 'frequency employed and the angle of reflection desired.

In accordance with the teachings of the present invention smallreflectors are now designed which have the behaviour of an infiniteconducting plane. We may compare it with the efficiency of a beam oflight and a reflectng mirror. A beam of light being very short in wavelength makes the reflecting mirror infinitely greater in dimension.Howeven in microwaves this'isnot the case. Here a reflector for examplemight be 3 feet or a meter wide while the wave length of the radio wavemight be a matter of inches'or centimeters. These finite dimensions havehere tofore resulted in standing waves and unfavor-' able conditions onthe reflector. The present invention eliminates or nullifies the effectsof these unfavorable features.

Further objects and advantages of this invention, as well as theapparatus, arrangement, operation and method, will be apparent from thefollowing description and claims in connection with'th'e accompanyingdrawings, in which,

Figure 1 is a representation of the reflection of; 65

I creases with distance.

a wave from an infinite plane,"

Figure 2 is a fragmentary section of a fiat reflecting strip shown inrelation to a rectangular cartesian coordinate system,

Figure 3 is a graphical representation of horizontally polarized fieldsexisting in the neighborhood of the reflector of Figure 2,

Figure 4 is a graph indicating phase displacement resulting fromdifference in length of two reflector strips,

Figure 5 is a fragmentary end section of a reflector embodying onefeature of this invention and showing a phase shifting end thereof,

Figure 6 is a reflector polar diagram showing reflected power andpercentage of maximum efficiency versus change of direction for a seriesof stated frequencies,

Figure 7 is a reflector cartesian diagram showing reflected power andpercentage of maximum efficiency versus the change of frequency for aseries of stated directions,

Figure 8 is a cartesian diagram showing unsymmetry when the antenna ismoved with respect to the reflector and the source of the waves,

Figure 9 is a cartesian diagram showing diffraction effects for anunsymmetrical position such as shown in Figure 8,-

Figure 10 is a cartesian diagram showing the unsymmetrical condition inrelation to the refiector when the antenna alsomoVes-out of the -XYplane, I

.Figure 11 is a fragmentary section type reflecting strip for avertically polarized field, and embodying another feature of thisinvention,

Figure 12 is a graphical representation, similar to Figure 3, showingthe field patterns existing upon a wing type reflecting strip asshownir- Figure 11, and

the wing type reflecting strip of Figure 11.

.A finite plane is considered one where the wave length of theelectromagnetic wave which is to be reflected, is a substantialdimension with respect to the length of the reflector itself. This isthe case in radio or radar on any frequency thus far employed. Usually awave arriving on a finite conducting surface sets up a standing wavesystem so that this surface acts like a scatterer and radiates power inall directions. The reflected field is not a plane field, i. e. withparallel wave fronts, but is a spherical field with sphericalconcentrical wave fronts.

The difference in efficiency of a scattering system, i. e. a finiteplane, versus that of an optical system, i. e. an infiinite plane,greatly inof a wing Figure 1 illustrates an optical reflection wherein Srepresents the source of energy; A rep resents the receiver or antenna;C is the plane of the reflector; B is the point at which the power fromS strikes the reflector; a is the useful area of the receiver; b is thearea of a reflector of finite dimensions in the reflecting .plane C; s.is an imaginary source of energy situated on the other side of thereflector and symmetrical to the real source S; is the angle ofincidence; T1 is the distance from the source S to the point ofreflection B, and m is the distance from the point of reflection B tothe receiverA.

Example-In the radar case, where the distance from the detecting vesselto the target vessel (1'1) is the same as from the target vessel back tothe detecting vessel (r2), assume the distance each way to be 10 miles.(See Figure 1.)

Then using Equations 1 and 4 derived in Part lot the following sectionon theory the finite and infinite cases compute as follows:

Power Infinite case K! In (r plus m2 KI l2.56 (10 plus 10) 2 Power Z=3l3.'6 times This indicates that under ideal conditions of reflection,the reflected power will be at least 313 time'sgreat'er in the aboveexample for an infinite surface as compared to a finite surface. X Thisdifference is less pronounced when the distances are less and isincreasingly greater as the distances are more than those mentioned inthe example above.

For communication purposes the reflector may be used under conditionswhere the outgoing signal instead of returning to the source as in thecase of radar, proceeds onward inja new direction in order to reach a"receiving location at a remote location that may be beyond or around anobstructed horizon. There the distance from the transmitting source toreflector (f1) would not necessarily be the same as the distancefromjrefiector to receiving point or a subsequent reflector (r2). V

ExampZe.-Assume n is miles while 1": is 20 miles.

Finite case Power Infinite case KI 12.56 (10 plus 20 2 K! 11304 ratio ofefiici'ency=approximately I In simple words, it may be stated that inthe finite case the power falls off inversely to the square of 4 pitimes the product of 1'1 and r2 squared. In the infinite case the powerfalls off only 4 pi (not 4 pi squared) times the sum squared (not theproduct squared) of Tl and This important difference in efiiciencyresults from the fact that in the finite case the arriving plane wavesystem is absorbed and scatters to become a new spherical system. Thisnew spherical system propagates in all directions. In the infinite case,however, the arrivimg plane wave system still remains a plane wavesystem after reflection, propagating in a Power =486.4 times directionsymmetrical to that of the arriving system (see Figure l).

A plane system of electromagnetic waves does not change its planecharacteristics if in any point in space, the Maxwell equations (i. e.the equations which are the basis of electromagnetic propagation) can besatisfied by the equations of a plane wave propagation, both for theelectric field and for the magnetic field. Maxwell's equations providein every point of space, some kindof equilibrium between the electricfield and the change of the magnetic field; and a similar balancebetween the magnetic field and the change of the electric field. It isinconsequential if this change is a displacement current or a conductioncurrent. The Equations 27 given in the following section on theoryrepresent a. field satisfying Maxwells equations.

In the case of an abrupt change of the means of propagation, like forthe presence of a conducting surface, it is necessary to substitute thedisplacement current in the space beyond the conducting surface with theactual conduction current on the surface in order to maintain thebalance with the magnetic field at the surface. In the case of a singlearriving system, this balance can be maintained only with the additionalpresence of a refiectedsystem, so that the resulting field will bebalanced by the current set up by the first system in the conductingsurface. If this conducting surface has to reflect a plane system, thecurrents which circulate in it must be such as to balance the fieldresulting from thesimultaneous presence of an arriving plane wave systemand a reflected one. Y

The following section on theory shows that this can be done by properchoosing of the shape of the refiector and the characteristics of thefield. A field polarized in the plane containing the source and thecenterof the reflector requires a flat sheet, (see "Part II theory) asin Figure 2, wherein 2| represents a fragmentary section of a flatreflecting sheet having a width of 2n, and being in the YZ plane.

A field polarized perpendicularly to that plane requires the addition oftwo wings of definite width to the same fiat'sheet (see Part V) as inFigure ll, wherein the reflecting sheet 2| is provided with a wing'22ofa width m upon each edge. The wings 22 are shown parallel to the XYplane 5. While the reflecting sheet 2| is in the YZ plane, 1. e. thewings 22 are perpendicular to the reflector 2 I.

In both cases the nearest end of the reflector 2| and the opposite oneshould be cut in a series of pr jecting Strips 23 of a definite length(see-Parts III and V theory) as in Figures 5 and 13 in order to, insuretheproper distribution of currents near a discontinuity such as the endof the conducting surface. Figure 5 shows a fragmentary end section of aflat reflector 2| having a series of projecting strips 23 extending fromthe end. The space 24 between the strips 23 is of the same width as thestrip 23. The projecting strips 23 may be considered as merelyextensions of imaginary trip 25 indicated by dotted lines extending thecomplete length of the reflector. The adjacent portion 26 of thereflector may then be considered as a similar strip of shorter length.Each strip 25 and the adjacent strip 26 forms a socalled phase shiftingcouple, the purpose of which will be more fully explained below. Thereflector is composed of one or more of these phase shifting couples.

In the case of the Wing reflector, each projecting strip 23 must carryits own wings of the same width as the side ones 22 (Figure 13). Thepart A of Figure 13 shows a fragmentary section of one embodiment of thewing type reflector wherein 2| is a flat reflecting sheet havingprojecting strips 23 extending from the ends as in Figure 5. Thisreflector also has wings 22 perpendicular to each outer edge as inFigure 11, and further has wings 21 of the same width as the wings 22upon each of the side edges of the projecting strips 23 alsoperpendicular thereto.

Figure 1313 shows another embodiment of the wing type reflector which isidentical to that of Figure 13A with the exception of the closed endsupon the strips 23. Closures 28 are provided upon the outer ends of thestrips 23 between the Wings 21, and closures 29 are provided at theinner ends.

The length of the projecting end strips 23 and the width of the wings 22are stated by the theor Equations 28 and 48:

Ay 4 4 cos 0 4 sin 0 where delta y is the length of the projecting strip23, m is the width of the wings 22 or 21, A (lambda) is the wavelengthin free space, M is the wavelength along the reflector, and 0 (theta) isthe reflection angle.

The phase displacement resulting in a length difference of i M Ay- 4between two strips is illustrated in Figure 4. The direct current waveis shown by a full line and the reflected wave is shown by the dottedline. It is seen that the reflected waves are 180 or completely .out ofphase on the two strips. Their fields thus destroy each other so thatthe total effect will be lack of back radiation. The reflector of thisinvention may be considered as consisting of a number of such stripseach pair of which comprises an elementary or unit reflector. Thenarrower the strips, the better will be the result. Therefore upon theactual reflector a plurality of pairs of the phase shifting strips orunit reflectors are used. The resulting shape of the re-,

flector is shown in Figure 5, which shows one end of a reflector inwhich twelve of the phase shifting couples or unit reflectors areemployed. The other end of the reflector is of similar construction. Areflector of this design is suitable for use with a horizontallypolarized field.

For a vertically polarized field a wing of a width corresponding toone-quarter of the wavelength in free space divided by the sine of themust be added to each edge of the flat reflector and to each edge of theend strips perpendicular to the said edges (see Figure 11). The wings ofeach elementary end strip may be either left open or closed by aconducting wall at their ends (see Figure 13).

In this case the reflector acts like a mirror which beams the radiationin a direction symmetrical to the source, i. e. with angle of reflectionequal to angle of incidence. It is clear thatthe strips which form theso-called phase shifting end and the wings must be tuned both forfrequency and direction. A change of frequency or a change of directionaffects the efiiciency of the reflector. The eifect of these changes maybe plotted as in Figures 6 and 7.

Figure 6 is a polar diagram showingthe change of reflected power andpercentage efliciency vs. change of direction for a series of statedfrequencies. Figure '7 is a cartesian diagram showing the change ofreflected power and percentage efliciency vs. the change of frequencyfor a series of stated directions. In both graphs the term frequencyomega sub zero appears. This is the cutoff frequency of the reflector.The cut-off frequency is that frequency which would have the maximumpower reflection at zero reflection angle, where reflection no longeroccurs. This is the lowest frequency that the reflector is able toreflect with maximum eiiiciency.

By dividing the speed of light or radio (approximately 300,000,000meters per second) by the cutoff frequency, we obtain the cut-offwavelength. It has to be pointed out that the cut-off wavelength is fourtimes longer than the strips which. make the phase shifting end; i. e.the phase shift-' ing end is one quarter of the cut-off wavelength. Thatis, if the reflection angle 0:0, using the equation frequency. It isdone by finding out the inter-t section of the curve identified by thedesired frequency, with a line drawn from the left corner (center of thepolar diagram) and making the desired angle with the abscissa. Thelength of the radius from the center to this point, transferred oneither side of the graph indicates directly the percentage ofefficiency. The best reflection angle for every frequency and its valueis written under the line which departs from the most external point ofevery curve.

As an example of the use of Figure 6, assume that the desired reflectionangle is 45 degrees-and that a frequency 1.3 timesthe cut-.offirequencyis .used. A line is thendra'wn from the leftlc'orner which makes anangle of 45 degrees with the abscissa. The intersection of this linewith the curve labeled 1.3 is now marked Using the length of the linefrom the centerto this point as aradius an arc is laid off on the chart.The percentage of efficiency is read from either axis where the arc cutsthe axis. In the case of 45 the efliciency is found to be approximately97%. Using an angle of reflection of 60 and the same frequency (1.3times the cut-off value) the efficiency of the reflectoris found to beapproximately 72%.

"By using Figure '7, it is possible to determine how thereflectionefficiency changes bychanging the frequency for a series of statedangles. ihis graphmay be useful if F. M. is used on the reflected beam.It is clear that the change of efficiency is negligible if the frequencydeviation is percentually small with respect to the carrier and if thecarrier is near the maximum efliciency frequency for that angle.

For example, taking a reflection angle of 60 and a frequency of 1.3times the cut-off frequency, using Figure 7, a line is drawn normal tothe abscissa at the point marked 1.3 on the frequency scale. Fromthe-point at which this line intersects the 60 curve a line isdrawn-parallel to theabscissa. The percent eflici'enoy is read from thepoint at which this line intersects the ordinate. Using a frequency of1.3 the efflciency is found to be approximately 72%. Using a frequencyof 1.6 times the cut-off frequencyand an angle of 60 the efiiciency isfound to be approximately 89%. Likewise a frequency of Z-times thecut-off frequency is found to be 100% eflicient with an angle of 60.

It is also pointed out that the reflection efficiencies plotted inFigures 6 and 7 refer to a direction symmetrical to that of the directbeam, namely to the direction in which light would be reflected if thereflector was a mirror. In this case it is obvious that the lightintensity would decrease abruptly simply by moving off the reflectedlight beam.

The. same thing happens with themicrowave reflected beam. Figures 6 and'7 give the; reflection efliciency for the center of the reflected beam.Moving away from this direction, the reflected power decreases tooalthough not so abruptly as in the case of the light beam. This isbecause of secondary lobes due to diffraction. Diflration in turn is dueto the fact that, the dimensions of the reflector are comparable withthe wave length. The smaller the reflector, the greater will be thisdiffraction efiec-t. Diffraction in this case may be defined as thedeviation of the radio beam from a straight course resulting fromthe-edge effect of a relatively small reflecting surface.

Large reflectors therefore should be usedfor concentrating power innarrow beams. Small reflectors, should be used for distributing powerinwider beams particularly where several possible positions of; a mobilestation are tobe covered with a single reflector. If a singlereflectoris not suficient to cover all positions of the movable station,several reflectors may be used as needed to integrate each other-bymeansof; secondary lobes. In this, case it might be a compound twistedreflector.

If reflectors are bent in order to, accomplish any type of focusing,defocusing or beaming effects in free space or near any kind ofradiating or receiving device, a definite reflection angle will appearat :every point of the reflector -between the direction of "the powerflow and the plane which is tangent to the reflector at tha't point.

'If' the field is such asto requirea'wing r flector, the Width of thewings must be tuned at every point with'regard'tothe actual reflectionangle at thatpoint ifmaximum eflicie-ncy is to'be obtained. Similarlythe lengthof 'the p'hase shifting end must. be tuned with regard to thereflection angle, measured betweenthe direction of "the .power flow and.the plane tangent to the reflector at' the end.

some of the many advantages and novel features of the present inventionare listed as folows:

-1 The reflector functions with a hi'gh'degree of efficiency with simpleforms and shapes -such as a. flat. surface for horizontally polarizedwaves. Horizontally. polarized field means that the elec tric. vector isparallel to'the plane of reflection, i. e. the plane which contains thesource, the reflector and the receiver.

2. It functions efflciently with the sameshape and surface. providedwings. are addedf'or vertically polarized waves. Vertically polarizedfieldhere means. thatv the electric vector is .perpendicularto saidplane.

3. The efileiency depends. upon the length of thephase shifting. endwhich must be tuned, -i. 6. formed or cut to that-size. accordingtothe-ire.- Quenovemployecl and the. reflection angle.

4.. Phase shiftin endsv aroused to avoid the existence of standing Wavesof current along the, reflector. Standing waves result in back radiationacross the source and low reflection efficiency.

5.- Phasing ends are. also used with curved or bent reflectors.

6. Th fiat reflectors; be used for distant reflecting a ound a corner.an. obstruction, or to extend the useful horizon.

7- The ent re lector or curved. reflector may be ed r any kind of focuin defocusing, 0r beaming effects in free space 'ornear any kind. ofradiating or receiving device.

8. The efliciency of an infinite plane is obtained with a plane offlnitedimensions, by the use of phasing ends only for a horizontally polarizedfield. By the addition of Wings, this is also possible for a verticallypolarized field.

9. Standing waves resulting from edge or discontinuity effects areeliminated.

10'. Attenuation is: less since the power at the receiver variesinversely with 4 pi times the square of the sum of the distances fromthe source. to the reflector and from the reflector-to the receiverinstead of varying inversely as the square of 4 pi times the product ofthe two distances.

THEORY Part L 'l' 'h.e .generaZ case The problem of transmission ofradiation. power from asource to a load (receiving antenna. array, horn,etc.) after a reflection over a. conducting-- surface, is completelysolved when the. reflector is a perfectly conducting; plane. of, in,-finite width and length.

This case isanalogous to an optical reflection as shown inFigure 1. Thereceiving. device A looks into the arriving reflected power as, if, itcame from a virtualjsource S situated on the other side of thereflecting plane, symmetrical to the real one S.

If a is assumed to be the equivalent useful area of the receivingdevice. being in a plane perpendicular to the line drawn from A to S (i.e. to the direction of the reflected power flow), the power crossing ais:

where P! is the total radiated power Pa. is the power crossing a n andT2 are the distances of S and A respectively from the point B Bis thepoint where the line from A to S crosses the reflector Equation 1 mustbe multiplied by G5 (gain factor of the source) if this has adirectional emission.

Now assume 11 so large as to result in practically plane waves where thereflection takes place,

The power given by (1) is the power that strikes the reflector aroundthe point Bover an area which is the projection of a from S on the planeof the reflector so that any other part of the reflector does notreflect useful power from S to a but, if the whole reflector is replacedwith any part of it which contains the projection of a witha finitearea, for example 12, which is even larger than the projection, thenEquation 1 no longer is correct. This is because the field which arrivesat B sets up in the 12 area currents that depend upon the shape of b andthe characteristics of the field itself. In a general case, thesecurrents result in standing waves which radiate the entire arrivingpower (the reflector being a perfect conductor) with a directionalpattern that is dependent in turn upon the distribution of the current.If Gs is the directional factor of the radiation from b to a, the powerreflected on a is:

where Pb is the total power radiated by I). But,

This value is far lower than that given by Equation 1.

The proper field andthe proper shape of b,

in order to reproduce with a finite reflector "the reflectioncharacteristics of an infinite reflecting plane will nowbe worked out.

Part II.--Plane reflector with, one limited dimension. Reflecting stripConsider a rectangular cartesian coordinate system as shown in Figure 2and let the ZY plane be the reflecting plane. A and S are assumed uponthe positive X side of it, both lying in the XY plane so that thepositive Y direction makes the smallest angle with the power flowdirection, both direct and reflected.

Then the width of the reflecting plane may be limited between twoparallel lines, so as to have a reflecting strip between zzin, where nequals one-half the width of the strip.

If this strip has to act as an infinite plane in the whole space betweenthe two planes e +n and 2 -11, then the field mustbe the same as in thecase of the infinite plane. then:

(a) Be composed of a direct plane wave sys tem and a reflected one (b)Propagate in directions parallel to the XY plane (0) Have the electricfield vector parallel to the X axis in the vicinity of the YZ plane (d)Have the magnetic field vector parallel to the YZ plane in the vicinityof it v (e) Have the magnetic field vector along the lines 2:11, 1: 0and z:n, zc=0 (i. e. the edges of the strip) perpendicular to them,because there the current may flow only in the Y direction (1) SatisfyMaxwells equations Mathematically, these requirements are expressed inthe following equations: in which,

The field must where F1, F2 are functions of the whole variable inbrackets.

Then the partial derivative of any element of the field inrespect to amust be equal to zero;

(7) Operator =0 (8) Ez=Ey= 0 at X=0 at any time (d) (9) H:c=0 at cc=0 atany time (e) (10) H1120 at x=0, Z=in at any time (I) d E d E d 1 (FE 11)W 8F W E 7a plus two similar equations for H.

From (6) it follows that Hy=0 not only *along the z=-* -n, :c=0 lines,but everywhere at the surface of the strip (:c=0); therefore dH, d6

1 I Now, from one of Maxwells equations the equivalent to (12) follows:

Applying (5) to the Ez component to the electric field, knowing that anyperiodic function F may be considered as a sum of a number of sine lawcomponents, it is sufficient to consider:

6 sin :z sin y cos c c which fits with (8) but sin 0 :0 sin 6 y cos 0) cw[cos w t+ C c which is equal to zero only when (if 0:0 there is noreflection). So it is seen that the plane wave system must be polarizedin the XY plane Consider now, vector E as the sum of Ex and Ey.

It will be:

(20) EI=E cos 0 (21) Ey E sin a both for the direct and for thereflected waves. But, 01' for the reflected wave is equal to 1r-0 (i. e.1800) for the direct wave. If F1 and F2 are both simple sine functionsbecomes:

a: sin 0 y cos 0) E sin w tthen (23) E=Eo cos 6 sin wA-J-Eo cos 0 sin wBE =Eo sin 0 sin wAE0 sin 0 sin wB whereAandBare:

(24) A=t+ c It is apparent that (2'7) fits with Maxwells equations (11)and (12). This is then a field which meets all of the aboverequirements. The E vector being always parallel to the XY plane,

a plot of it can be drawn that is only in theXY plane. This is shown inFigure 3 where-the lower part shows the direct wave system, themiddlepart the resulting fleld near the reflector, and the upper part thereflected Wave system. The arrows behind the reflector show the motionof the whole field configuration and the vector composition of thevelocities. The pattern is frozen at time i=0. It is now apparent that aplane reflector with only one limited dimension may act in the samemanner as a reflector of infinite dimensions.

Part III.Plane reflector with two limited dimansions. Reflecti'ng stripof finite length. Phase shifting couple If a piece of reflecting stripis cut to a given length, with both ends to reflect back along the stripthe current waves which move along it as an effect of the moving field;the reflected cur rent waves will build up a damped (because of theenergy loss due to radiation) wave system. If the reflected currentwaves moving back in the -Y direction have the same shapeand speed ofthe direct ones, their energy will be radiated back in the direction ofthe direct field. This will be weakened by the exact amount of powerwhich is connected with the reflected current waves, and which istotally lost for the reflected field. The performance of the reflectorbecomes lower through the effect of an abrupt ending of the strip.

Comparing the phases of the reflected current waves in two reflectorstrips with a length difference of At 1 A 1/2 211 0r 21- cos.

where ya and y1 are the respective lengths of the two strips it is thewave length along the strip and A is the wave length in free space 0 isthe reflection angle it is seen that there is a phase shift 0f 1rradians or This means the two reflected waves are completely out ofphase as shown in Figure e where the full line shows the direct currentwave, while the dotted lines show the reflected one. Their fields willthen destroy each other, so that the total effect will be lack of backradiation. The narrower the strips, then the better will be the result.In order to have a considerable amount of reflected power, several pairsof phase shifting strips may be used. The resulting shape of thereflector will then be as shown in Figure 5.

Part I V.-Directional effects of the phase shifting edge Both a changeof A and a change of 0 may produce a change of M, which in turn bringsthe reflected current waves slightly back in phase again. This resultsin back radiation and lower performance of the whole reflector. CallingAy the length difference between the phase shifting strips, the backreflected power P.. is then:

and the reflected power P ,4:

8 P P @=P0(1-'$Hl COSZED Where P0 is the power that would be reflected'13 in the case of perfect tuning conditions and 6 is the re-phasingangle between the two currents.

Now

where M is the original wave length along the strip, and A: is the newone. But by construction it is so that referring to A (33) (A in freespace) therefore (30) becomes:

( PTB=PO cos (g -213% cos 0) =P sin (211- cos 6) a known value. It isthen possible to plot PP, vs. 0 for every 40.

We may call 00 that value of w which makes and label our patterns interms of in order to be free from actual measurements as Ay and A. SeeFig. 6.

At the same time Pkg vs. may be plotted for every 0. This graph may beuseful to determine what band of frequencies may be reflected on the sambeam with a reasonably small change of power (see Figure 7).

But, (34) with Figures 6 and 7, refer to what happens nearthe edge ofthe reflector. If the whole length of the reflector is considered, it isapparent that the reflected power is greater on any 01' because of theattenuation of the reflected currentwave system, and of the possiblereflection of the opposite edge of the reflector. Both of these reducethe back radiation along the strip (where the arriving power isconstant). Depending on the actual length of the reflector, the patternsof Figure 6 and Figure '7 may be somewhat more rounded. and flat.

It must be pointed out that in Figures 6 and '7, 0; for the reflectedwave is equal to 1r0 or 180--@ for the-direct one. This means that thepower ismeasured in a direction which is symmetrical to that of thearriving power.

Figures 8 and 9 represent cases wherein the antenna A is in the samehorizontal plane (1. e. the XY plane) as the reflected power but is in adifferent vertical plane from that containing the line representingreflected power. The power arriving at the reflecting plane makes anangle of 6 with this plane and is reflected at an angle of 1-0 ('1800).The antenna A is in a direction of 5 from the reflecting plane whichdiffers from 71'-6 by an angle of a.

Figure 10 shows an instance in which the antenna A lies in a verticalplane differing from that containing the line representing reflectedpower by an angle of a (as in Figures 8 and 9). but in which the antennaA lies outside of the XY plane. The line in the A direction in this casemakes an angle of ,8 with the XY plane.

In Figures 9 and 10 the length of the reflector is 2L and the width is2n.

Now, considering Figure 8, if the power is measured in a directiondiflerent from 1r-0, (34) no longer holds. This may happen when S (or A)moves with respect to the reflector while A (or S) does not move, orwhen both move in an unsymmetrical manner. In this case (34) will holdonly in the 11-0 direction, while in the direction, the power may beevaluated as described below.

Consider Figure 9 in which a reflector 2L long is excited by a fieldarriving from the 0 direction. The reflected power in the 1r0 directionis given by (34), which power will be present at the front of thereflected wave when leaving the reflector. This wave front is f=F1-F. Byapplying the Huyghens-Fresnel principle to this wave-front, we canevaluate the-power per unit cross-length proceeding in the direction, onthe XY plane.

This power per unit cross length will be proportional to the square ofthe resulting electric field at a distance so great as to makenegligible the range differences from any point of the wavefront I. Theresulting electric field is then proportional to the mean value of Eover j, which is:

f fOOSaSina E fcos -d m fcosa 0 w c fOOSzx cE f sin 0: cos a sin a (37)wf cos a sin 0: c

and the total power crossing the new wave front will be 0 W 2 .sin 2a(38) Pa P1-a f Sin2 a sin wf 20 but (39) f=2L sin a (on the XY plane)then c wL sin 0 sin 20: 2

2 sin (2W sin 26)) 15 then L n 2 x2 [sln (2r Slll 2a sin 6 s1n Z'IIK$111 25 :l If.) 4x sin 6 sin a sin 6 This shows that the reflected powerpropagates in a narrow beam with the axis symmetrical to the directionof the direct power flow. Along this beam the power is given (in firstapproximation) by (34), but moving away from it both in the XY plane andout of it, the power decreases rapidly, as given by (46).

Now it is seen that (34) gives only the power crossing the wave frontwhile leaving the reflector. Actually this is the reflected power andnot the propagating power in the 1r0 direction. This reflected powerthen propagates with a pattern as given by (46) This means that thepower arriving at a receiving device placed in 1r-H direction (i. e.a=0, 3=0), at a distance so great as to make L and n negligible, is lessthan that given by (34), because a part of it has gone in other(a=0,;9=0) directions.

In a very narrow beam with most of the power arriving in the 1r-0direction (a=0,/3=0) is desired L, n must be large. If a broad beam, isdesired with distributed power on a large area around the (a=0,;3=0)direction, L 11. must be kept small.

Part V.Z-poZarieed field, wing reflector It has been shown that a planereflector requires an XY polarized field. Now it will be seen that a Zpolarized field may be handled by means of a suitably bent reflectingsurface.

The total reflection of a Z polarized field requires that the X and Ycomponents of the electric vector be everywhere and always equal tozero. However, the electric vector near a conducting surface must bezero, or perpendicular to the conducting surface. The magnetic vectormust be parallel to it, and perpendicular to the edge of the conductingsurface. (See section 2, Equations 5, 6, 7 and 8 for everywhere.Equations 9 and 10 for the edges. If edges are still parallel to theY-axis see Equations 11 and 12.)

It has already been determined that a Z polarized field is impossiblewith a plane reflecting strip. But, if two perpendicularly bent wings,are added to the strip at the edges, forming a C cross section (as shownin Figure 11), with both of these wings being of proper and equal width(m) then the Z polarized field is possible. Now (10) holds for z in, mand the following must be added:

It is now apparent that (1'7) fits all conditions provided:

(48) 771-4 sin 9 which is necessary to satisfy the boundary conditionsfor H, while and (21) do not hold any more.

This may be also obvious by considering the reflector as the half of awave guide excited in the TEm mode. The free presence of the field alongthe cut is balanced by the direct and reflected fields in the externalspace. The resulting field patterns are shown in Figure 12 where we cansee the magnetic lines of force in the XY plane, using the same methodof portrayal as in Figure 3.

.16 On the right side of the. figure, is shown the electric fleld in theXZ plane.

It is then possible to apply Parts III and IV to this case with noimportant change. It is sufficient to point out that the wings of eachelementary reflector may be either (a) left open or (1)) closed by aconducting wall of their ends. See Figure 13.

VI.--Cylindrical reflectors (non-plane) For focusing or defocusingeffects, both around a transmitting or receiving device, or in anywave-optical problem, the reflector may be bent as required, getting acylindrical surface, with the generatrices parallel to the Z-axis andany cross section over the XY plane. But, while a reflecting strip mayreflect any XY field at any 0 along its whole length, and requires aproper adjustment only in the phase shifting ends (according to theactual 0 at the end), a wing reflector can not totally reflect a Z fieldin any direction, even if carefully tuned in its phase shifting ends.This is because of (48). which requires the tuning of m along the wholelength of the reflector according to the actual 0 at every point of it.

This leads to the design of high performance beaming devices with veryhigh directional gain factors.

What is claimed is:

1. A microwave reflector comprising a continuous flat reflecting sheethaving at the ends thereof a plurality of projecting strips disposed inthe plane of said reflector and of a length substantially equivalent toone quarter of the wave length at the operating frequency.

2. A reflector for ultra-high-frequency waveenergy comprising acontinuous reflection medium having a plurality of coplanar projectionsat each end thereof, said projections being of a length substantiallyequivalent to where Ay is the length of the projecting strips, and M isthe wave length at the operating frequency.

3. A microwave reflector, comprising a central body portion and a pairof end portions, said end portions comprising a plurality of rectangularprojections mutually spaced a distance substantially equal to theirwidth and of a length substantially equivalent to where Ay is the lengthof the projections, A is the wave length in free space for the frequencyinvolved, and 0 is the angle of reflection.

4. A reflector for a vertically polarized field comprising a bodyportion, and perpendicularly disposed flanges of width substantiallyequivalen to l 4 sin 0 where m is the width of the flanges, A is thewave length in free space for the frequency involved and 6 is thereflection angle, said flanges being secured to opposite edges only ofsaid body portion.

5. A microwave reflector for a vertically polarized field comprising abody member, a plurality of strips integral and coplanar with said bodymember and mutually spaced apart a distance 17 approximately equal totheir width and of a length substantially equivalent to where Ay is thelength of the projecting strips, k is the wave length in free space forthe frequency involved, and is the angle of reflection, and flanges atthe edges of the said body member and the edges of the said strips, saidflanges being disposed perpendicularly relative said body member andsaid strips and having a width k 4 sin 0 where m is the width of thesaid flanges and A and 0 are again wave length in free space for thefrequency involved and reflection angle, respectively.

6. Microwave apparatus comprising a smooth continuous reflector, and atleast one pair of reflecting strips integral with said reflector, ateach end of said reflector and coplanarly disposed with respect thereto,the strips of each pair being laterally spaced from each other adistance equal to the width of a single strip.

'7. Microwave apparatus comprising a smooth continuous reflector, atleast one pair of reflecting strips integral with said reflector. ateach end of said reflector and coplanarly disposed with respect to saidreflector, and flanges upstanding from the free edges of said reflectorand said strips.

8. Microwave apparatus comprising a continuous reflector, at least onepair of reflecting strips integral with said reflector, at each end ofsaid reflector and coplanarly disposed with respect 18 to saidreflector, and flanges upstanding from the lateral edges of saidreflector and said strips.

9. Microwave apparatus comprising a continuous reflector, a plurality ofreflecting strips integral with said reflector, at each end of saidreflector and coplanarly disposed with respect thereto, the strips ofeach pair being laterally spaced from each other a distance equal to thewidth of a single strip, and flanges upstanding from the free edges ofsaid reflector and strips.

10. The apparatus as defined in claim 9, wherein said flanges are ofuniform width and proportional to the length of the waves to bereflected therefrom.

11. The apparatus as defined in claim 9 wherein said strips are of equallength and proportional to the length of the waves to be reflectedtherefrom.

SAMUEL FREEDMAN. GIUSTO FONDA BONARDI.

REFERENCES CITED The following references are of record in the file ofthis patent:

UNITED STATES PATENTS Number Name Date 1,906,546 Darbord May 2, 19332,270,314 Kraus Jan. 20, 1942 2,271,300 Lindenblad Jan. 27, 19422,281,196 Lindenblad Apr. 28, 1942 2,434,893 Alford et a1 Jan. 2'7, 19482,480,154 Masters Aug. 30, 1949 FOREIGN PATENTS Number Country Date802,728 France Sept. 14, 1936

